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In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem for suspension flows and give a new proof of Gutman-Jin embedding theorem.
We study two coupled discrete-time equations with different (asynchronous) periodic time scales. The coupling is of the type sample and hold, i.e., the state of each equation is sampled at its update times and held until it is read as an input at the
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of attractor,
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form, and in th
Let $mathcal{M}(X)$ be the space of Borel probability measures on a compact metric space $X$ endowed with the weak$^ast$-topology. In this paper, we prove that if the topological entropy of a nonautonomous dynamical system $(X,{f_n}_{n=1}^{+infty})$